+ iq>^RIHtHt^RIHt^RIHt^RIHt^RI H t ^RI H t ^RI Ht^RIHt^R IHt^R IHt^R IHt^R IHt^R IHt^RIHt^RIHt^RIH t !RR]!4t"!RR]"]]] ] ]]]]]]]]]4t#R#))gtlt)xrange)SpecialFunctions)RSCache)QuadratureMethods) LaplaceTransformInversionMethods)CalculusMethods)OptimizationMethods) ODEMethods) MatrixMethods)MatrixCalculusMethods)LinearAlgebraMethods)Eigen)IdentificationMethods)VisualizationMethods)libmpc]tRt^tRtR#)ContextN)__name__ __module__ __qualname____firstlineno____static_attributes__ro/Users/tonyclaw/.openclaw/workspace/skills/math-calculator/venv/lib/python3.14/site-packages/mpmath/ctx_base.pyrrsrrcfa]tRt^to]P t]P tRtRtRt Rt Rt Rt Rt RtRtR tR tR tR tR tR!RltR"RltRtR#RltR$RltR%RltRtRtRtRtRt] !]PB4t"] !]PF4t#] !]PH4t$] !]PJ4t%] !]PL4t&] !]PN4t(] !]PR4t*] !]PV4t,] !]PZ4t.R&Rlt/R&Rlt0Rt1Rt2Rt3Rt4R t5Vt6R#)'StandardBaseContextc/Vn\P!V4\P!V4\P!V4\ P!V4\ P!V4\P!V4R#N)_aliasesr__init__rrr r r )ctxs&rr#StandardBaseContext.__init__*s] !!#&""3'(11#6  %s#rc VPP4Fwr\W\W44K R# \dK/i;ir!)r"itemssetattrgetattrAttributeError)r$aliasvalues& r _init_aliases!StandardBaseContext._init_aliases4sCLL..0LE GC$781"  s< A  A Fc\RV4R#)zWarning:N)printr$msgs&&rwarnStandardBaseContext.warn@s  j#rc\V4hr!) ValueErrorr1s&&r bad_domainStandardBaseContext.bad_domainCs orcB\VR4'd VP#V#)real)hasattrr:r$xs&&r_reStandardBaseContext._reFs 1f  66MrcV\VR4'd VP#VP#)imag)r;rAzeror<s&&r_imStandardBaseContext._imKs! 1f  66MxxrcV#r!rr<s&&r _as_pointsStandardBaseContext._as_pointsPsrc &VPV4)#r!convert)r$r=kwargss&&,rfnegStandardBaseContext.fnegSs Arc PVPV4VPV4,#r!rIr$r=yrKs&&&,rfaddStandardBaseContext.faddV{{1~ckk!n,,rc PVPV4VPV4, #r!rIrOs&&&,rfsubStandardBaseContext.fsubYrSrc PVPV4VPV4,#r!rIrOs&&&,rfmulStandardBaseContext.fmul\rSrc PVPV4VPV4, #r!rIrOs&&&,rfdivStandardBaseContext.fdiv_rSrc V'dCV'd\RV4VP4#\RV4VP4#V'd\RV4VP4#\WP4#)c3F"TFp\V4^,xK R#5iNabs.0r=s& r +StandardBaseContext.fsum..es4t!CFAIIts!c38"TFp\V4xK R#5ir!rarcs& rrerffs-1Asc32"TF q^,xK R#5ir_rrcs& rrerfhs+d1ds)sumrB)r$argsabsolutesquareds&&&&rfsumStandardBaseContext.fsumbs_ 4t4chh??--sxx8 8 +d+SXX6 64""rNcaVe \W4pV'd-VPo\V3RlV4VP4#\RV4VP4#)Nc3F<"TFwrVS!V4,xK R#5ir!r)rdr=rPcfs& rre+StandardBaseContext.fdot..ps0REQ"Q%Rs!c36"TFwrW,xK R#5ir!r)rdr=rPs& rrerrrs,s)zipconjrirB)r$xsys conjugaterqs&&&&@rfdotStandardBaseContext.fdotksK >RB B0R0#((; ;,,chh7 7rc@VPpVF pW#,pK V#r!)one)r$rjprodargs&& rfprodStandardBaseContext.fprodts!wwC KD rc >\VP!W3/VB4R#)z& Equivalent to ``print(nstr(x, n))``. N)r0nstr)r$r=nrKs&&&,rnprintStandardBaseContext.nprintzs chhq&v&'rc aaSf^dSP,oSPV4p\V4p\V4S8d SP#SP V4'dp\ SVS,4p\VP 4V8d VP#\VP4V8dSP^VP 4#V# \du\TSP4'dTPTT3Rl4u#\TR4'd+TUu.uFpSPTS4NK Muupiupu#T#i;i)a~ Chops off small real or imaginary parts, or converts numbers close to zero to exact zeros. The input can be a single number or an iterable:: >>> from mpmath import * >>> mp.dps = 15; mp.pretty = False >>> chop(5+1e-10j, tol=1e-9) mpf('5.0') >>> nprint(chop([1.0, 1e-20, 3+1e-18j, -4, 2])) [1.0, 0.0, 3.0, -4.0, 2.0] The tolerance defaults to ``100*eps``. c(<SPVS4#r!)chop)ar$tols&r*StandardBaseContext.chop..s!S)9r__iter__)epsrJrbrB_is_complex_typemaxrAr:mpc TypeError isinstancematrixapplyr;r)r$r=rabsxpart_tolrsf&f rrStandardBaseContext.chops ;cgg+C 5 AAq6D1v|xx##A&&sDH-qvv;)66Mqvv;)771aff--   5!SZZ((ww9::q*%%234!QC(!44&  5s57CC*8C#5C=EE0E  EEc 2VPV4pVf*Vf&VP^VP)^,4;r4VfTpMVfTp\W, 4pWT8:dR#\V4p\V4pWg8d WW, pW8*#WV, pW8*#)a Determine whether the difference between `s` and `t` is smaller than a given epsilon, either relatively or absolutely. Both a maximum relative difference and a maximum difference ('epsilons') may be specified. The absolute difference is defined as `|s-t|` and the relative difference is defined as `|s-t|/\max(|s|, |t|)`. If only one epsilon is given, both are set to the same value. If none is given, both epsilons are set to `2^{-p+m}` where `p` is the current working precision and `m` is a small integer. The default setting typically allows :func:`~mpmath.almosteq` to be used to check for mathematical equality in the presence of small rounding errors. **Examples** >>> from mpmath import * >>> mp.dps = 15 >>> almosteq(3.141592653589793, 3.141592653589790) True >>> almosteq(3.141592653589793, 3.141592653589700) False >>> almosteq(3.141592653589793, 3.141592653589700, 1e-10) True >>> almosteq(1e-20, 2e-20) True >>> almosteq(1e-20, 2e-20, rel_eps=0, abs_eps=0) False T)rJldexpprecrb) r$strel_epsabs_epsdiffabssabsterrs &&&&& ralmosteqStandardBaseContext.almosteqsB KKN ?w # !chhYq[ 9 9G ?G _G13x ?1v1v ;)C~)C~rc \V4^8:g\R\V4,4h\V4^8g\R\V4,4h^p^p\V4^8Xd V^,pM"\V4^8dV^,pV^,p\V4^8Xd V^,pVPV4VPX4VPV4r4pW#,V8wgQR4hW$8dV^8d.#\pMV^8d.#\p.p^pTpW#V,,pV^, pV!W4'dVP V4K:V#)a This is a generalized version of Python's :func:`~mpmath.range` function that accepts fractional endpoints and step sizes and returns a list of ``mpf`` instances. Like :func:`~mpmath.range`, :func:`~mpmath.arange` can be called with 1, 2 or 3 arguments: ``arange(b)`` `[0, 1, 2, \ldots, x]` ``arange(a, b)`` `[a, a+1, a+2, \ldots, x]` ``arange(a, b, h)`` `[a, a+h, a+h, \ldots, x]` where `b-1 \le x < b` (in the third case, `b-h \le x < b`). Like Python's :func:`~mpmath.range`, the endpoint is not included. To produce ranges where the endpoint is included, :func:`~mpmath.linspace` is more convenient. **Examples** >>> from mpmath import * >>> mp.dps = 15; mp.pretty = False >>> arange(4) [mpf('0.0'), mpf('1.0'), mpf('2.0'), mpf('3.0')] >>> arange(1, 2, 0.25) [mpf('1.0'), mpf('1.25'), mpf('1.5'), mpf('1.75')] >>> arange(1, -1, -0.75) [mpf('1.0'), mpf('0.25'), mpf('-0.5')] z+arange expected at most 3 arguments, got %iz+arange expected at least 1 argument, got %iz0dt is too small and would cause an infinite loop)lenrmpfrrappend) r$rjrdtbopresultirs &* rarangeStandardBaseContext.arangesE@4yA~I!$i() )4yA~I!$i() )   t9>QA Y!^QAQA t9>aB771:swwqz3772;bv{NNN{ 5Av BAv B  qDA FA!xx a  rc n\V4^8XdDVPV^,4pVPV^,4p\V^,4pM\V4^8XdU\V^,R4'gQhV^,PpV^,P p\V^,4pM\ R\V4,4hV^8d \R4hRV9dVR,'dlV^8XdVPV4.#WC, VPV^, 4, p\V4Uu.uFqwV,V,NK ppWHR&V#WC, VPV4, p\V4Uu.uFqwV,V,NK ppV#uupiuupi)aT ``linspace(a, b, n)`` returns a list of `n` evenly spaced samples from `a` to `b`. The syntax ``linspace(mpi(a,b), n)`` is also valid. This function is often more convenient than :func:`~mpmath.arange` for partitioning an interval into subintervals, since the endpoint is included:: >>> from mpmath import * >>> mp.dps = 15; mp.pretty = False >>> linspace(1, 4, 4) [mpf('1.0'), mpf('2.0'), mpf('3.0'), mpf('4.0')] You may also provide the keyword argument ``endpoint=False``:: >>> linspace(1, 4, 4, endpoint=False) [mpf('1.0'), mpf('1.75'), mpf('2.5'), mpf('3.25')] _mpi_z*linspace expected 2 or 3 arguments, got %izn must be greater than 0endpoint) rrintr;rrrr6r) r$rjrKrrrsteprrPs &*, rlinspaceStandardBaseContext.linspace sl* t9>Q AQ ADG A Y!^47G,, ,,Q AQ ADG AH!$i() ) q578 8V#vj'9'9Av |#ESWWQU^+D%+AY/Y4!YA/bEESWWQZ'D%+AY/Y4!YA/ 00s F-F2c NVP!V3/VBVP!V3/VB3#r!)cossinr$zrKs&&,rcos_sinStandardBaseContext.cos_sinNs)wwq#F#SWWQ%9&%999rc NVP!V3/VBVP!V3/VB3#r!)cospisinpirs&&,r cospi_sinpiStandardBaseContext.cospi_sinpiQs)yy%f%syy'=f'===rcP\RVR,,^V,,4#)ig?)r)r$ps&&r_default_hyper_maxprec*StandardBaseContext._default_hyper_maxprecTs4!T'>AaC'((rc*VPp^ pW4,^,VnVPpVPp^pV!4FppWh, pWr,'gOV'dGVPV4p \ WY4pVPV4p W, VP8dM V^, pKr VX , p W8wdM8W8gVP 'dMV\ VPV 4, pKVW0n# Y0ni;i )rninfrBmagr_fixed_precisionmin) r$terms check_stepr extraprecmax_magrktermterm_magsum_mag cancellations &&& rsum_accurately"StandardBaseContext.sum_accuratelyasxx I+a/((HH!GDIANN#&774="%g"8"%''!*"-8!FA$ '0 /+s/C/C/CS<88 HtHsAD 'A:D "!D Dc0VPp^ pW4,^,VnVPpVPpTp^pV!4Fqp Wy,pW, p W,'gHVPV 4p \ W[4pVPWv, 4p V )VP8dM V^, pKs VX , p W8wdM8W8gVP 'dMV\ VPV 4, pKVW0n# Y0ni;ir)rrr|rrrr)r$factorsrrrrr|rrfactorrrrrs&&& rmul_accurately"StandardBaseContext.mul_accurately}sxx I+a/((gg%iFKA!>> from mpmath import * >>> mp.dps = 30; mp.pretty = True >>> power(2, 0.5) 1.41421356237309504880168872421 This shows the leading few digits of a large Mersenne prime (performing the exact calculation ``2**43112609-1`` and displaying the result in Python would be very slow):: >>> power(2, 43112609)-1 3.16470269330255923143453723949e+12978188 rI)r$r=rPs&&&rpowerStandardBaseContext.powers {{1~Q//rc$VPV4#r!)zeta)r$rs&&r _zeta_intStandardBaseContext._zeta_intsxx{rc &aaaa^.oVVVV3RlpV#)a Return a wrapped copy of *f* that raises ``NoConvergence`` when *f* has been called more than *N* times:: >>> from mpmath import * >>> mp.dps = 15 >>> f = maxcalls(sin, 10) >>> print(sum(f(n) for n in range(10))) 1.95520948210738 >>> f(10) # doctest: +IGNORE_EXCEPTION_DETAIL Traceback (most recent call last): ... NoConvergence: maxcalls: function evaluated 10 times c<S^;;,^, uu&S^,S8dSPRS,4hS!V/VB#)rz%maxcalls: function evaluated %i times) NoConvergence)rjrKNcounterr$fs*,rf_maxcalls_wrapped8StandardBaseContext.maxcalls..f_maxcalls_wrappedsC AJ!OJqzA~''(ORS(STTd%f% %rr)r$rrrrsfff @rmaxcallsStandardBaseContext.maxcallss # & & "!rc daaa/oVVV3RlpSPVnSPVnV#)a Return a wrapped copy of *f* that caches computed values, i.e. a memoized copy of *f*. Values are only reused if the cached precision is equal to or higher than the working precision:: >>> from mpmath import * >>> mp.dps = 15; mp.pretty = True >>> f = memoize(maxcalls(sin, 1)) >>> f(2) 0.909297426825682 >>> f(2) 0.909297426825682 >>> mp.dps = 25 >>> f(2) # doctest: +IGNORE_EXCEPTION_DETAIL Traceback (most recent call last): ... NoConvergence: maxcalls: function evaluated 1 times c<V'dV\VP443pMTpSPpVS 9dS V,wrEWC8dV5#S!V/VBpW63S V&V#r!)tupler'r) rjrKkeyrcpreccvaluer,r$rf_caches *, rf_cached-StandardBaseContext.memoize..f_cachedsfE&,,.1188Dg~ ' ="7Nt&v&E =GCLLr)r__doc__)r$rrrsff @rmemoizeStandardBaseContext.memoizes.( JJ99rr)FF)NF)r!)NN))7rrrrrr ComplexResultr#r-rverboser3r7r>rCrFrLrQrUrXr[rmryrrrrrrrrr staticmethodgcd_gcd list_primesisprimebernfracmoebiusifac_ifaceulernum _eulernum stirling1 _stirling1 stirling2 _stirling2rrrrrrr__classdictcell__) __classdict__s@rrrsJ''M''M$G  ----#8 ( "H1fGR,\:>)  "Du001K5==)GENN+H5==)G  $EU^^,Ieoo.Jeoo.J8@0$"0$$rrN)$operatorrr libmp.backendrfunctions.functionsrfunctions.rszetarcalculus.quadraturercalculus.inverselaplacer calculus.calculusr calculus.optimizationr calculus.odesr matrices.matricesr matrices.calculusrmatrices.linalgrmatrices.eigenridentificationr visualizationrrobjectrrrrrr#sv!1%2E.6%,41!1/ f V' $ Vr